In a unanimously agreed statement, the 15-member council said it was of vital importance that North Korea shows "sincere commitment to denuclearisation through concrete action and stressed the importance of working to reduce tensions".
North Korea's launch of a longer-range missile shows advances in its technological capabilities and offers the sternest test yet of President Donald Trump's strategy to work with China to combat the threat.
"We will conduct ICBM tests anytime and anywhere in accordance with the decisions made by our central leadership", North Korea's ambassador to China Ji Jae Pyong said.
Moon met Matt Pottinger, overseeing Asian affairs at the U.S. National Security Council, on Tuesday and said he hoped to continue to have "sufficient, close discussions" between Seoul and Washington, the Blue House press secretary told a briefing.
The UN Security Council first imposed sanctions on North Korea in 2006 in response to its five nuclear tests and two long-range rocket launches.
Turkey's Foreign Ministry also condemned the missile launch in a written statement.
The series of launches has raised global alarms as the North has warned of firing an intercontinental ballistic missile which could be capable of reaching the Unites States, or of conducting a sixth nuclear test despite pressure from the worldwide community to refrain from doing so.
The missile was launched on an unusually high trajectory, before splashing down in the Sea of Japan (East Sea).
Although outside experts see several places where North Korea is likely stretching the truth, the missile launched Sunday appears to be the most powerful the country has ever tested.
North Korea's foreign ministry rejected the statement, saying it infringed on its right to self-defense, particularly as the missile was sacked at a sharp angle to ensure the safety of neighboring countries.
Russian President Vladimir Putin called North Korea's latest missile test "counter-productive, harmful and unsafe".
That could be a thinly veiled shot at the USA -led sanctions regime against North Korea. Pundits believe Pyongyang's latest provocation will provide a hard litmus test for South Korea's newly-elected President Moon Jae-in.
It says the "era of strategic patience" with North Korea is over.
After North Korea's latest missile test, the White House released a statement highlighting how close the missile came to Russian soil - and noting "the President can not imagine that Russia is pleased".
Putin said: "We are categorically against the expansion of the club of nuclear powers".
North Korea said it fired the missile at a high angle to avoid neighboring countries.
Moon, South Korea's first liberal leader in almost a decade, said as he took his oath of office last week that he'd be willing to visit North Korea if the circumstances were right.
Each new nuclear and longer-range missile test is part of the North's attempt to build a nuclear-tipped intercontinental ballistic missile. During his campaign, President Moon had promised to take a softer policy approach on North Korea, pursuing peaceful dialogue and constructive engagement with the regime.